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On increasing-failure-rate random variables

Part of: Distribution theory Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Sheldon M. Ross ,
J. George Shanthikumar  and
Zegang Zhu
Sheldon M. Ross*
Affiliation:
University of Southern California
J. George Shanthikumar*
Affiliation:
University of California, Berkeley
Zegang Zhu*
Affiliation:
University of California, Berkeley
*
∗Postal address: Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, 3715 McClintock Avenue, GER 240, Los Angeles, CA 90089-0193, USA. Email address: smross@usc.edu
∗∗Postal address: Department of Industrial Engineering and Operations Research, 4135 Etcheverry Hall, University of California, Berkeley, CA 94720, USA.
∗∗Postal address: Department of Industrial Engineering and Operations Research, 4135 Etcheverry Hall, University of California, Berkeley, CA 94720, USA.
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Abstract

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We provide sufficient conditions for the following types of random variable to have the increasing-failure-rate (IFR) property: sums of a random number of random variables; the time at which a Markov chain crosses a random threshold; the time until a random number of events have occurred in an inhomogeneous Poisson process; and the number of events of a renewal process, and of a general counting process, that have occurred by a randomly distributed time.

Keywords

Stochastic orderingIFR propertyDRHR propertyrenewal processMarkov chain

MSC classification

Primary: 62E10: Characterization and structure theory
Secondary: 60E15: Inequalities; stochastic orderings
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 797 - 809
Copyright
© Applied Probability Trust 2005 

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